Modelo matemático para o sistema oscilante de glicina catalisado pelo complexo NiL(ClO4)2

Abstract

In 2010, an oscillating system was reported that constitutes a variant of the Belousov-Zhabotinskii reaction (BZ), in which the organic substrate are both the amino acid glycine and acetone, catalyzed by a nickel II tetraazomacrocyclic complex, NiL(ClO4)2. The objective of this work was to develop a simple mathematical model in the form of a nonlinear EDO's system that describes the oscillating system described above using a proposed mechanism and the concentration intervals observed experimentally for which oscillations are observed, with a view to the established FKN model. From a proposed mechanism, a transient model of 15 variables was elaborated, whose numerical analysis showed that, for this system, the catalyst does not play an important role in the mathematical description of oscillations. Based on these results and using approximations, a stationary model of three variables was obtained. The three-variable model was numerically explored to determine the concentration intervals for which oscillations are observed, showing that it has a limit cycle. It was not possible to predict exact intervals, but oscillating behavior was observed in values close to those obtained experimentally for bromine, glycine and H+, but not for acetone, due to approximations. The model presents limitations but can describe dynamic behavior and can be improved and explored through stability analysis in future work.